Symmetry enforced fractonicity and $2d$ quantum crystal melting

TL;DR

This paper introduces the concept of symmetry enforced fractonicity in 2D crystals, showing how it affects quantum melting transitions and leads to novel phases like super-solids and super-nematic states.

Contribution

It develops a dual tensor gauge theory framework to analyze symmetry enforced fractonicity and reveals new quantum melting scenarios in 2D crystals.

Findings

Strong quantum fluctuations favor super-solid formation.

Dislocation condensation leads to super-nematic phase.

Quantum melting differs from classical Halperin-Nelson scenario.

Abstract

Fractons are particles that cannot move in one or more directions without paying energy proportional to their displacement. Here, we introduce the concept of symmetry enforced fractonicity, in which particles are fractons in the presence of a global symmetry, but are free to move in its absence. A simple example is dislocation defects in a two-dimensional crystal, which are restricted to move only along their Burgers vector due to particle number conservation. Utilizing a recently developed dual rank-2 tensor gauge description of elasticity, we show that accounting for their symmetry enforced one-dimensional nature of dislocation motion dramatically alters the structure of quantum crystal melting phase transitions. We show that, at zero temperature, sufficiently strong quantum fluctuations of the crystal lattice favor the formation of a super-solid phase that spontaneously breaks the symmetry enforcing fractonicity of defects. The defects can then condense to drive the crystal into a super-nematic phase via a phase transition in the $2+1d$ XY universality class to drive a melting phase transition of the crystal to a nematic phase. This scenario contrasts the standard Halperin-Nelson scenario for thermal melting of $2d$ solids in which dislocations can proliferate via a single continuous thermal phase transition. We comment on the application of these results to other scenarios such as vortex lattice melting at a magnetic field induced superconductor-insulator transition, and quantum melting of charge density waves of stripes in a metal.